Question

Let $0<a<b<c$ be $3$ distinct digits. The sum of all $3$ -digit number formed by using all the $3$ digits one each is $1554$. The value of $c$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (B)

$4$

The three digit numbers formed by using $a,b,c$ once each are

$abc,acb,bca,bac,cab,cba$

Sum of these numbers is $222(a+b+c)$

Which is equal to $1554\left(given\right)$

$a+b+c=7,$ since $0<a<b<c$, the only possible set for $(a,b,c)$ is

$(1,2,4)$, So the value of c is $4$